The phenomenon known in cognitive psychology as U-shaped behavioral growth is discussed in relation to second language learning. The U-shaped growth concept focuses on the fact that some behaviors appear, disappear, and then apparently reappear over time. It has been documented in children's learning of physical concepts, musical concepts, artistic production, and first language acquisition. This paper focuses on the conditions under which U-shaped curves might occur, and especially on the role played by cross-linguistic influence. The data are drawn from some experiments conducted in the Netherlands and Finland with advanced second language learners. It is maintained that U- shaped learning behavior can be characterized as the external manifestation of a more general cognitive process. Further, it is suggested that U-shaped language development in both first and second language occurs in the area of morphology, in phraseology, and especially in connection with the learning of lexical items that covey complex semantic relations. Contains 13 references. (LB)